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Grade Change Length Calculator

Work out grade change length instantly with clear inputs, formula shown and shareable results.

About Grade Change Length Calculator

Vertical curve length is specified as a K value, the length per percent of algebraic grade change, which encodes the sight distance requirement for the design speed. Multiplying K by the algebraic difference gives the minimum length, subject to an absolute minimum for appearance and drainage, typically 0.6 times the design speed in metres.

Formulas

Minimum length

L = K x algebraic difference in grade, subject to an absolute minimum

Curve type

A falling algebraic difference gives a crest curve, a rising one a sag curve

Worked example

With the default values below, Grade Change Length Calculator returns Minimum vertical curve length of 150.00. Change any input above and every figure here is recalculated in your browser.

Inputs used

Incoming gradeaccepts -20–20 %
3 %
Outgoing gradeaccepts -20–20 %
-2 %
K value for the design speedminimum 1 m per %
30 m per %
Absolute minimum curve lengthminimum 1 m
40 m

Results

Minimum vertical curve length
150.00 m
Algebraic difference in grade
5.00 %
Length from the K value
150.00 m
Curve type
Crest curve — sight distance governs

Step by step

  1. 1Values used
  2. 2Minimum length
  3. 3Curve type
  4. 4Minimum vertical curve length= 150.00 m
  5. 5Algebraic difference in grade= 5.00 %
  6. 6Length from the K value= 150.00 m
  7. 7Curve type= Crest curve — sight distance governs

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
  • Preliminary estimate only. Vertical curve design must follow the geometric design standard adopted by the road authority.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Preliminary estimate only. Vertical curve design must follow the geometric design standard adopted by the road authority.

Frequently Asked Questions

How is the Grade Change Length figure worked out?

L = K x algebraic difference in grade, subject to an absolute minimum. Vertical curve length is specified as a K value, the length per percent of algebraic grade change, which encodes the sight distance requirement for the design speed.

Why do crest and sag curves have different K values?

Crests are governed by stopping sight distance over the hump. Sags are governed by headlight throw at night and by passenger comfort, so the required K values differ for the same speed.

What values do I need to enter?

This calculator takes 4 inputs: Incoming grade, Outgoing grade, K value for the design speed, Absolute minimum curve length. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.

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